As mentioned previously, the flight data recorder found inside the Pentagon appeared to be missing its last 4-8 seconds of data. This had been one of the minor technical mysteries associated with the terrorist attacks of 11 September 2001.
That mystery has been solved by an Australian computer scientist/programmer named Warren Stutt. Working on his own as an unofficial and independent investigator, Stutt decided to take a fresh look at the raw binary data from the flight data recorder (FDR). After studying over 600 pages of mind-numbing technical documentation, and writing his own software to decompress/decode that data, Stutt succeeded in recovering four more seconds at the end of the FDR data. These last seconds were from an incomplete data frame with bad parity, which may explain why previous software had failed to recover them.
The new data end with a radar height of 4 feet and the most rapid deceleration the FDR could record, as though the aircraft had hit something big and solid. A dip in the longitudinal acceleration 3/4 second before the end may correspond to the clipping of light poles 4 and 5.
In my earlier review of a really bad propaganda video, I used several mathematically idealized trajectories to show that flight 77 could have cleared the Navy annex and struck the Pentagon in level flight without exceeding the capabilities of a Boeing 757. The new FDR data show that terrorist pilot Hani Hanjour flew a more erratic approach that did not quite achieve level flight.
Although the FDR recorded pressure altitude and radio height only once per second, a more detailed picture of flight 77's final approach can be reconstructed from the accelerometer data, which were recorded 8 times per second (for the vertical acceleration) or 4 times per second (for the longitudinal and lateral accelerations):
The graph above was obtained by treating the altitude as a function of time, and finding the curve for that function by solving an initial value problem that essentially uses the accelerations recorded by the FDR to simulate the flight backwards.
The initial values consist of the aircraft's position and velocity at the end of its data. I took the x-y position to be the origin, and the altitude (z) to be the height of the Pentagon lawn above sea level. The velocity involved a little guesswork: My initial guess came from running the last recorded velocity forward to the end of data as an initial value problem. I then adjusted that guess slightly to improve the match between the shape of the calculated altitude and the shape of the pressure altitude.
In theory, one could simulate the entire flight backwards. In practice, however, my simulation begins to diverge from the recorded pressure altitude and radio height a little over one minute from the end of the flight.
The main source of this divergence appears to be the absence of any corrective feedback in my algorithm.
My numerical solution of the initial value problem is inherently unstable for exactly the same reason that dead reckoning becomes inaccurate over long distances: the errors tend to add up over time. The accumulation of error could be corrected using feedback to bring the calculated altitude back into line with the recorded pressure altitude and radio height, but that seems pointless in this case: We already know the recorded pressure altitude and radio height, and we also have radar data that tell us the aircraft's position and altitude up until its radar return disappeared into ground clutter during its final seconds. Since the final seconds were the only ones for which we did not know the altitudes, and my unsophisticated open-loop solution of the initial value problem is adequate for the final seconds, I didn't bother to add a feedback mechanism.
Although pitch and roll angles were recorded by the FDR, the best fit between the calculated solution and the position/altitude/height data recorded by the FDR was obtained by ignoring the pitch and roll angles. That may mean the acceleration data were corrected for pitch and roll before they were sent to the FDR for recording.
Another possibility is that small calibration and alignment errors may be responsible. Examination of the data reveals some small but systematic errors in pitch angle and/or accelerometer calibration/alignment, and it may have been just a matter of chance that omitting the correction for pitch in my calculations for the last few seconds reduced the influence of those errors. I will look into this further.
The accelerations recorded by the FDR show that the inexperienced terrorist pilot, Hani Hanjour, flew very erratically, reacting late and over-correcting:
The pilot's interventions become even more frenetic during the final minute:
The accelerations recorded during the last five seconds show an apparent impact with something solid at -.25 seconds, and may also show an impact with something less substantial at -.75 seconds:
The longitudinal acceleration shown at -.25 seconds is the most extreme negative acceleration the FDR was capable of recording, so the actual deceleration was probably more severe than recorded. This may correspond to impact with the generator trailer, or possibly to impact with the Pentagon itself.
The dip in longitudinal acceleration at -.75 seconds may have been caused by impacts with the 4th and 5th light poles, which would have occurred during that quarter-second interval. The first and second light poles were struck near their tops, which means they would have acquired less momentum, which means those impacts are unlikely to show up in the acceleration data.
The software I wrote for this essay is written in R6RS Scheme and was run in Larceny:
csv.slsparses the comma-separated-value (CSV) files produced by Warren's program
integrate77.slssolves the initial value problem by performing a crude numerical integration
graph-alt-vs-x.spscreated data files for the altitude versus distance graphs
graph-acc-vs-t.spscreated data files for the acceleration versus time graphs
makedatfiles.shcreated the data files by running the Scheme programs
makejpgfiles.shcreated the JPEG files using
All flight data used here come from the flight data recorder as decoded using Warren Stutt's software. All of us who have been interested in the final seconds of flight 77 owe Warren a great deal of thanks for recovering the final seconds from the compressed/encoded data file provided years ago by the NTSB.
I am also indebted to engineer John Farmer, who is writing a book on this and related subjects, and to a number of knowledgeable and helpful people who hang out at the James Randi Educational Foundation's discussion forum.
William D Clinger
Last updated 16 February 2010.